Visible crew/equipment: When the pursuing police car exits the sewer, two mannequins can be seen in the driver and passenger seats. (00:42:35)
The Gauntlet - S1-E4
Visible crew/equipment: While Macgyver is running into the desert, a camera is visible in the far right of the screen. (00:05:07)
Visible crew/equipment: As they drive the car out of the plane with a parachute you can also see someone else (another camera man probably) jump out right behind the car in the same shot. (00:45:30 - 00:46:05)
Flame's End - S1-E13
Visible crew/equipment: As Amy and MacGyver are chased around a nuclear reactor just before the bad guy gets nuclear steam on him, you can see a pair of legs in a top row window around where they are walking. Remember the nuclear reactor was hot with radiation so no-one would be wandering around.
Visible crew/equipment: Early in the episode a thumb/finger is visible at the bottom of the screen turning the timer wheel simulating a working timer that is actually just a dummy prop, a few seconds before it explodes. (00:02:39)
Ghost Ship - S3-E4
Visible crew/equipment: MacGyver is repairing the broken boat to get to the abandoned ship. When he leaves the shore and starts to paddle towards the ship, you can see a boom mic drop into the picture from top left. (00:09:15)
Answer: Late one night, Geoffrey used a covert listening device to overhear David explaining his barricade device to Janet which is how he figured it out.
How do we know Geoffrey really did use a covert listening device? They didn't mention him using one.
There was a scene of him using it when David told Janet about his barricade.